Recent developments in CNNs have provided promising results for many applications in machine learning and computer vision such as facial recognition [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, image retrieval [4]}, [8]}, [9]}, [10]}, image generation [11]}, [12]}, [11]}, and adversarial attack [14]}, [15]}. However, the success of CNN models requires a vast amount of well-annotated training data, which is not always feasible to perform manually [16]}, [17]}. There are essentially two different solutions that are usually used to deal with this problem: 1) Transfer Learning (TL) and 2) Semi-Supervised Learning (SSL). In TL methods [18]}, the learning of a new task is improved by transferring knowledge from a related task which has already been learned. SSL methods [19]}, however, tend to learn discriminative models that can make use of the information from an input distribution that is given by a large amount of unlabeled data. To make use of unlabeled data, it is presumed that the underlying distribution of data has some structure. SSL algorithms make use of at least one of the following structural assumptions: continuity, cluster, or manifold [20]}. In the continuity assumption, data which are close to each other are more likely to belong to the same class. In the cluster assumption, data tends to form discrete clusters, and data in the same cluster are more likely to share the same label. In modern high-dimensional settings which are typical in signal processing [21]}, [22]} or genomics [23]}, [24]}, [25]}, low-dimensional representation of the data are difficult. For example, in parallel with machine learning advances, Mohamadi et al [23]} present a new trend in signal processing on non-stationary data, where jointly model the linear and non-linear characteristics of time series. In their work as a pioneer work, they discuss how joint linear and non-linear of modeling by ARIMA-GARCH modeling allows accurate prediction of of biomedical time series. They also extend their framework to other interesting application such as genomic [25]} which prove the capability of this pioneer framework. However, in the manifold assumption, data lies approximately on a manifold of much lower dimension than the input space which can be classified by using distances and densities defined on the manifold. Thus, to define a natural similarity distance or divergence between probability measures on a manifold, it is important to consider the geometrical structures of the metric space in which the manifold exists [28]}.
